SOLUTION: Consider a right triangle. The length of the long side is 23 longer than the short side. The length of the hypotenuse is 2 longer than the long side. What is the length of the long

Algebra ->  Triangles -> SOLUTION: Consider a right triangle. The length of the long side is 23 longer than the short side. The length of the hypotenuse is 2 longer than the long side. What is the length of the long      Log On


   

Question 316427: Consider a right triangle. The length of the long side is 23 longer than the short side. The length of the hypotenuse is 2 longer than the long side. What is the length of the long side?
b =
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Use the Pythagorean theorem,
A%5E2%2BB%5E2=H%5E2
S%5E2%2B%28S%2B23%29%5E2=%28S%2B23%2B2%29%5E2
S%5E2%2B%28S%5E2%2B46S%2B529%29=%28S%5E2%2B50S%2B625%29
2S%5E2%2B46S%2B529=S%5E2%2B50S%2B625
S%5E2-4S-96=0
%28S-12%29%28S%2B8%29=0
Only the positive solution makes sense in this case,
S-12=0
Short:S=12
Long:L=S%2B23=35
Hypotenuse:H=L%2B2=37